Given that (6,-8) is on graph f(x), find the corresponding point for the function f(-1/2x)

Set the argument -1/2x equal to the x coordinate of the given point 6. Solve for x

-1/2x = 6
x = 6(-2)
x = -12

So x = -12 makes the equation -1/2x = 6 true. 

If we plug x = -12 into f(-1/2x) we get f(6)

Since we know that (6,-8) is on the graph of f(x), we know that (-12,-8) is on the graph of f(-1/2x)

What happens is that there's a reflection over the y axis (due to the minus sign in -1/2x) and there's a horizontal stretch by a factor of 2. So the graph of f(-1/2x) appears to be wider than f(x).

In summary, the final answer is (-12,-8)